Diffusion epidemic models with incubation and crisscross dynamics.

A diffusion age-structured epidemic model is analyzed. The model describes an epidemic in a host-vector two-population system. Each population is diffusing in a spatial region. Each population is divided into susceptible, incubating, and infectious subclasses. The incubating and infectious subclasses in each population are determined by a structure variable corresponding to age since infection. The model consists of a system of nonlinear partial differential equations with crisscross dynamics. The existence, uniqueness, and asymptotic behavior of solutions are analyzed.